mailitics

Category: stat.TH

  • Statistical and Algorithmic Foundations of Reinforcement Learning

    Statistical and Algorithmic Foundations of Reinforcement Learning arXiv:2507.14444v1 Announce Type: new Abstract: As a paradigm for sequential decision making in unknown environments, reinforcement learning (RL) has received a flurry of attention in recent years. However, the explosion of model complexity in emerging applications and the presence of nonconvexity exacerbate the challenge of achieving efficient RL…

  • When few labeled target data suffice: a theory of semi-supervised domain adaptation via fine-tuning from multiple adaptive starts

    When few labeled target data suffice: a theory of semi-supervised domain adaptation via fine-tuning from multiple adaptive starts arXiv:2507.14661v1 Announce Type: new Abstract: Semi-supervised domain adaptation (SSDA) aims to achieve high predictive performance in the target domain with limited labeled target data by exploiting abundant source and unlabeled target data. Despite its significance in numerous…

  • A Survey of Dimension Estimation Methods

    A Survey of Dimension Estimation Methods arXiv:2507.13887v1 Announce Type: new Abstract: It is a standard assumption that datasets in high dimension have an internal structure which means that they in fact lie on, or near, subsets of a lower dimension. In many instances it is important to understand the real dimension of the data, hence…

  • Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights

    Finite-Dimensional Gaussian Approximation for Deep Neural Networks: Universality in Random Weights arXiv:2507.12686v1 Announce Type: new Abstract: We study the Finite-Dimensional Distributions (FDDs) of deep neural networks with randomly initialized weights that have finite-order moments. Specifically, we establish Gaussian approximation bounds in the Wasserstein-$1$ norm between the FDDs and their Gaussian limit assuming a Lipschitz activation…

  • Choosing the Better Bandit Algorithm under Data Sharing: When Do A/B Experiments Work?

    Choosing the Better Bandit Algorithm under Data Sharing: When Do A/B Experiments Work? arXiv:2507.11891v1 Announce Type: new Abstract: We study A/B experiments that are designed to compare the performance of two recommendation algorithms. Prior work has shown that the standard difference-in-means estimator is biased in estimating the global treatment effect (GTE) due to a particular…

  • Physics-informed machine learning: A mathematical framework with applications to time series forecasting

    Physics-informed machine learning: A mathematical framework with applications to time series forecasting arXiv:2507.08906v1 Announce Type: new Abstract: Physics-informed machine learning (PIML) is an emerging framework that integrates physical knowledge into machine learning models. This physical prior often takes the form of a partial differential equation (PDE) system that the regression function must satisfy. In the…

  • Mallows Model with Learned Distance Metrics: Sampling and Maximum Likelihood Estimation

    Mallows Model with Learned Distance Metrics: Sampling and Maximum Likelihood Estimation arXiv:2507.08108v1 Announce Type: new Abstract: textit{Mallows model} is a widely-used probabilistic framework for learning from ranking data, with applications ranging from recommendation systems and voting to aligning language models with human preferences~cite{chen2024mallows, kleinberg2021algorithmic, rafailov2024direct}. Under this model, observed rankings are noisy perturbations of a…

  • Class conditional conformal prediction for multiple inputs by p-value aggregation

    Class conditional conformal prediction for multiple inputs by p-value aggregation arXiv:2507.07150v1 Announce Type: new Abstract: Conformal prediction methods are statistical tools designed to quantify uncertainty and generate predictive sets with guaranteed coverage probabilities. This work introduces an innovative refinement to these methods for classification tasks, specifically tailored for scenarios where multiple observations (multi-inputs) of a…

  • Enjoying Non-linearity in Multinomial Logistic Bandits

    Enjoying Non-linearity in Multinomial Logistic Bandits arXiv:2507.05306v1 Announce Type: new Abstract: We consider the multinomial logistic bandit problem, a variant of generalized linear bandits where a learner interacts with an environment by selecting actions to maximize expected rewards based on probabilistic feedback from multiple possible outcomes. In the binary setting, recent work has focused on…

  • Property Elicitation on Imprecise Probabilities

    Property Elicitation on Imprecise Probabilities arXiv:2507.05857v1 Announce Type: new Abstract: Property elicitation studies which attributes of a probability distribution can be determined by minimising a risk. We investigate a generalisation of property elicitation to imprecise probabilities (IP). This investigation is motivated by multi-distribution learning, which takes the classical machine learning paradigm of minimising a single…

  • Implicit Regularisation in Diffusion Models: An Algorithm-Dependent Generalisation Analysis

    Implicit Regularisation in Diffusion Models: An Algorithm-Dependent Generalisation Analysis arXiv:2507.03756v1 Announce Type: new Abstract: The success of denoising diffusion models raises important questions regarding their generalisation behaviour, particularly in high-dimensional settings. Notably, it has been shown that when training and sampling are performed perfectly, these models memorise training data — implying that some form of…

  • It’s Hard to Be Normal: The Impact of Noise on Structure-agnostic Estimation

    It’s Hard to Be Normal: The Impact of Noise on Structure-agnostic Estimation arXiv:2507.02275v1 Announce Type: new Abstract: Structure-agnostic causal inference studies how well one can estimate a treatment effect given black-box machine learning estimates of nuisance functions (like the impact of confounders on treatment and outcomes). Here, we find that the answer depends in a…

  • Disentangled Feature Importance

    Disentangled Feature Importance arXiv:2507.00260v1 Announce Type: new Abstract: Feature importance quantification faces a fundamental challenge: when predictors are correlated, standard methods systematically underestimate their contributions. We prove that major existing approaches target identical population functionals under squared-error loss, revealing why they share this correlation-induced bias. To address this limitation, we introduce emph{Disentangled Feature Importance (DFI)},…

  • GRAND: Graph Release with Assured Node Differential Privacy

    GRAND: Graph Release with Assured Node Differential Privacy arXiv:2507.00402v1 Announce Type: new Abstract: Differential privacy is a well-established framework for safeguarding sensitive information in data. While extensively applied across various domains, its application to network data — particularly at the node level — remains underexplored. Existing methods for node-level privacy either focus exclusively on query-based…

  • The final solution of the Hitchhiker’s problem #5

    The final solution of the Hitchhiker’s problem #5 arXiv:2506.20672v1 Announce Type: new Abstract: A recent survey, nicknamed “Hitchhiker’s Guide”, J.J. Arias-Garc{i}a, R. Mesiar, and B. De Baets, A hitchhiker’s guide to quasi-copulas, Fuzzy Sets and Systems 393 (2020) 1-28, has raised the rating of quasi-copula problems in the dependence modeling community in spite of the…

  • Lower Bounds on the Size of Markov Equivalence Classes

    Lower Bounds on the Size of Markov Equivalence Classes arXiv:2506.20933v1 Announce Type: new Abstract: Causal discovery algorithms typically recover causal graphs only up to their Markov equivalence classes unless additional parametric assumptions are made. The sizes of these equivalence classes reflect the limits of what can be learned about the underlying causal graph from purely…

  • Gaussian Processes and Reproducing Kernels: Connections and Equivalences

    Gaussian Processes and Reproducing Kernels: Connections and Equivalences arXiv:2506.17366v1 Announce Type: new Abstract: This monograph studies the relations between two approaches using positive definite kernels: probabilistic methods using Gaussian processes, and non-probabilistic methods using reproducing kernel Hilbert spaces (RKHS). They are widely studied and used in machine learning, statistics, and numerical analysis. Connections and equivalences…

  • Sampling conditioned diffusions via Pathspace Projected Monte Carlo

    Sampling conditioned diffusions via Pathspace Projected Monte Carlo arXiv:2506.15743v1 Announce Type: new Abstract: We present an algorithm to sample stochastic differential equations conditioned on rather general constraints, including integral constraints, endpoint constraints, and stochastic integral constraints. The algorithm is a pathspace Metropolis-adjusted manifold sampling scheme, which samples stochastic paths on the submanifold of realizations that…

  • On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiologic boundary conditions

    On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiologic boundary conditions arXiv:2506.11683v1 Announce Type: new Abstract: Solving inverse problems in cardiovascular modeling is particularly challenging due to the high computational cost of running high-fidelity simulations. In this work, we focus on Bayesian parameter estimation and explore different methods to reduce the…

  • Distributionally-Constrained Adversaries in Online Learning

    Distributionally-Constrained Adversaries in Online Learning arXiv:2506.10293v1 Announce Type: new Abstract: There has been much recent interest in understanding the continuum from adversarial to stochastic settings in online learning, with various frameworks including smoothed settings proposed to bridge this gap. We consider the more general and flexible framework of distributionally constrained adversaries in which instances are…

  • Assumption-free stability for ranking problems

    Assumption-free stability for ranking problems arXiv:2506.02257v1 Announce Type: new Abstract: In this work, we consider ranking problems among a finite set of candidates: for instance, selecting the top-$k$ items among a larger list of candidates or obtaining the full ranking of all items in the set. These problems are often unstable, in the sense that…

  • Overfitting has a limitation: a model-independent generalization error bound based on R’enyi entropy

    Overfitting has a limitation: a model-independent generalization error bound based on R’enyi entropy arXiv:2506.00182v1 Announce Type: new Abstract: Will further scaling up of machine learning models continue to bring success? A significant challenge in answering this question lies in understanding generalization error, which is the impact of overfitting. Understanding generalization error behavior of increasingly large-scale…

  • Riemannian Principal Component Analysis

    Riemannian Principal Component Analysis arXiv:2506.00226v1 Announce Type: new Abstract: This paper proposes an innovative extension of Principal Component Analysis (PCA) that transcends the traditional assumption of data lying in Euclidean space, enabling its application to data on Riemannian manifolds. The primary challenge addressed is the lack of vector space operations on such manifolds. Fletcher et…

  • Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Games

    Finite-Sample Convergence Bounds for Trust Region Policy Optimization in Mean-Field Games arXiv:2505.22781v1 Announce Type: new Abstract: We introduce Mean-Field Trust Region Policy Optimization (MF-TRPO), a novel algorithm designed to compute approximate Nash equilibria for ergodic Mean-Field Games (MFG) in finite state-action spaces. Building on the well-established performance of TRPO in the reinforcement learning (RL) setting,…

  • A Kernelised Stein Discrepancy for Assessing the Fit of Inhomogeneous Random Graph Models

    A Kernelised Stein Discrepancy for Assessing the Fit of Inhomogeneous Random Graph Models arXiv:2505.21580v1 Announce Type: new Abstract: Complex data are often represented as a graph, which in turn can often be viewed as a realisation of a random graph, such as of an inhomogeneous random graph model (IRG). For general fast goodness-of-fit tests in…

  • Learning with Expected Signatures: Theory and Applications

    Learning with Expected Signatures: Theory and Applications arXiv:2505.20465v1 Announce Type: new Abstract: The expected signature maps a collection of data streams to a lower dimensional representation, with a remarkable property: the resulting feature tensor can fully characterize the data generating distribution. This “model-free” embedding has been successfully leveraged to build multiple domain-agnostic machine learning (ML)…

  • Kernel Quantile Embeddings and Associated Probability Metrics

    Kernel Quantile Embeddings and Associated Probability Metrics arXiv:2505.20433v1 Announce Type: new Abstract: Embedding probability distributions into reproducing kernel Hilbert spaces (RKHS) has enabled powerful nonparametric methods such as the maximum mean discrepancy (MMD), a statistical distance with strong theoretical and computational properties. At its core, the MMD relies on kernel mean embeddings to represent distributions…

  • Online Statistical Inference of Constrained Stochastic Optimization via Random Scaling

    Online Statistical Inference of Constrained Stochastic Optimization via Random Scaling arXiv:2505.18327v1 Announce Type: new Abstract: Constrained stochastic nonlinear optimization problems have attracted significant attention for their ability to model complex real-world scenarios in physics, economics, and biology. As datasets continue to grow, online inference methods have become crucial for enabling real-time decision-making without the need…

  • Liouville PDE-based sliced-Wasserstein flow for fair regression

    Liouville PDE-based sliced-Wasserstein flow for fair regression arXiv:2505.17204v1 Announce Type: new Abstract: The sliced Wasserstein flow (SWF), a nonparametric and implicit generative gradient flow, is applied to fair regression. We have improved the SWF in a few aspects. First, the stochastic diffusive term from the Fokker-Planck equation-based Monte Carlo is transformed to Liouville partial differential…

  • Optimal Transport with Heterogeneously Missing Data

    Optimal Transport with Heterogeneously Missing Data arXiv:2505.17291v1 Announce Type: new Abstract: We consider the problem of solving the optimal transport problem between two empirical distributions with missing values. Our main assumption is that the data is missing completely at random (MCAR), but we allow for heterogeneous missingness probabilities across features and across the two distributions.…

  • Out-of-Distribution Generalization of In-Context Learning: A Low-Dimensional Subspace Perspective

    Out-of-Distribution Generalization of In-Context Learning: A Low-Dimensional Subspace Perspective arXiv:2505.14808v1 Announce Type: new Abstract: This work aims to demystify the out-of-distribution (OOD) capabilities of in-context learning (ICL) by studying linear regression tasks parameterized with low-rank covariance matrices. With such a parameterization, we can model distribution shifts as a varying angle between the subspace of the…

  • A Linear Approach to Data Poisoning

    A Linear Approach to Data Poisoning arXiv:2505.15175v1 Announce Type: new Abstract: We investigate the theoretical foundations of data poisoning attacks in machine learning models. Our analysis reveals that the Hessian with respect to the input serves as a diagnostic tool for detecting poisoning, exhibiting spectral signatures that characterize compromised datasets. We use random matrix theory…

  • An Exponential Averaging Process with Strong Convergence Properties

    An Exponential Averaging Process with Strong Convergence Properties arXiv:2505.10605v1 Announce Type: new Abstract: Averaging, or smoothing, is a fundamental approach to obtain stable, de-noised estimates from noisy observations. In certain scenarios, observations made along trajectories of random dynamical systems are of particular interest. One popular smoothing technique for such a scenario is exponential moving averaging…

  • Fairness-aware Bayes optimal functional classification

    Fairness-aware Bayes optimal functional classification arXiv:2505.09471v1 Announce Type: new Abstract: Algorithmic fairness has become a central topic in machine learning, and mitigating disparities across different subpopulations has emerged as a rapidly growing research area. In this paper, we systematically study the classification of functional data under fairness constraints, ensuring the disparity level of the classifier…

  • Sharp Gaussian approximations for Decentralized Federated Learning

    Sharp Gaussian approximations for Decentralized Federated Learning arXiv:2505.08125v1 Announce Type: new Abstract: Federated Learning has gained traction in privacy-sensitive collaborative environments, with local SGD emerging as a key optimization method in decentralized settings. While its convergence properties are well-studied, asymptotic statistical guarantees beyond convergence remain limited. In this paper, we present two generalized Gaussian approximation…

  • High-Dimensional Importance-Weighted Information Criteria: Theory and Optimality

    High-Dimensional Importance-Weighted Information Criteria: Theory and Optimality arXiv:2505.06531v1 Announce Type: new Abstract: Imori and Ing (2025) proposed the importance-weighted orthogonal greedy algorithm (IWOGA) for model selection in high-dimensional misspecified regression models under covariate shift. To determine the number of IWOGA iterations, they introduced the high-dimensional importance-weighted information criterion (HDIWIC). They argued that the combined use…

  • Optimal Regret of Bernoulli Bandits under Global Differential Privacy

    Optimal Regret of Bernoulli Bandits under Global Differential Privacy arXiv:2505.05613v1 Announce Type: new Abstract: As sequential learning algorithms are increasingly applied to real life, ensuring data privacy while maintaining their utilities emerges as a timely question. In this context, regret minimisation in stochastic bandits under $epsilon$-global Differential Privacy (DP) has been widely studied. Unlike bandits…

  • Categorical and geometric methods in statistical, manifold, and machine learning

    Categorical and geometric methods in statistical, manifold, and machine learning arXiv:2505.03862v1 Announce Type: new Abstract: We present and discuss applications of the category of probabilistic morphisms, initially developed in cite{Le2023}, as well as some geometric methods to several classes of problems in statistical, machine and manifold learning which shall be, along with many other topics,…

  • From Two Sample Testing to Singular Gaussian Discrimination

    From Two Sample Testing to Singular Gaussian Discrimination arXiv:2505.04613v1 Announce Type: new Abstract: We establish that testing for the equality of two probability measures on a general separable and compact metric space is equivalent to testing for the singularity between two corresponding Gaussian measures on a suitable Reproducing Kernel Hilbert Space. The corresponding Gaussians are…

  • Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networks

    Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networks arXiv:2505.01995v1 Announce Type: new Abstract: Individual treatment effect estimation has gained significant attention in recent data science literature. This work introduces the Double Neural Network (Double-NN) method to address this problem within the framework of extended fiducial inference (EFI). In the proposed method, deep…

  • Gaussian Differential Private Bootstrap by Subsampling

    Gaussian Differential Private Bootstrap by Subsampling arXiv:2505.01197v1 Announce Type: new Abstract: Bootstrap is a common tool for quantifying uncertainty in data analysis. However, besides additional computational costs in the application of the bootstrap on massive data, a challenging problem in bootstrap based inference under Differential Privacy consists in the fact that it requires repeated access…

  • Provable Efficiency of Guidance in Diffusion Models for General Data Distribution

    Provable Efficiency of Guidance in Diffusion Models for General Data Distribution arXiv:2505.01382v1 Announce Type: new Abstract: Diffusion models have emerged as a powerful framework for generative modeling, with guidance techniques playing a crucial role in enhancing sample quality. Despite their empirical success, a comprehensive theoretical understanding of the guidance effect remains limited. Existing studies only…

  • Inference for max-linear Bayesian networks with noise

    Inference for max-linear Bayesian networks with noise arXiv:2505.00229v1 Announce Type: new Abstract: Max-Linear Bayesian Networks (MLBNs) provide a powerful framework for causal inference in extreme-value settings; we consider MLBNs with noise parameters with a given topology in terms of the max-plus algebra by taking its logarithm. Then, we show that an estimator of a parameter…

  • Kernel Density Machines

    Kernel Density Machines arXiv:2504.21419v1 Announce Type: new Abstract: We introduce kernel density machines (KDM), a novel density ratio estimator in a reproducing kernel Hilbert space setting. KDM applies to general probability measures on countably generated measurable spaces without restrictive assumptions on continuity, or the existence of a Lebesgue density. For computational efficiency, we incorporate a…

  • Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels

    Learning Operators by Regularized Stochastic Gradient Descent with Operator-valued Kernels arXiv:2504.18184v1 Announce Type: new Abstract: This paper investigates regularized stochastic gradient descent (SGD) algorithms for estimating nonlinear operators from a Polish space to a separable Hilbert space. We assume that the regression operator lies in a vector-valued reproducing kernel Hilbert space induced by an operator-valued…

  • No-Regret Generative Modeling via Parabolic Monge-Amp`ere PDE

    No-Regret Generative Modeling via Parabolic Monge-Amp`ere PDE arXiv:2504.09279v1 Announce Type: new Abstract: We introduce a novel generative modeling framework based on a discretized parabolic Monge-Amp`ere PDE, which emerges as a continuous limit of the Sinkhorn algorithm commonly used in optimal transport. Our method performs iterative refinement in the space of Brenier maps using a mirror…

  • Can SGD Select Good Fishermen? Local Convergence under Self-Selection Biases and Beyond

    Can SGD Select Good Fishermen? Local Convergence under Self-Selection Biases and Beyond arXiv:2504.07133v1 Announce Type: new Abstract: We revisit the problem of estimating $k$ linear regressors with self-selection bias in $d$ dimensions with the maximum selection criterion, as introduced by Cherapanamjeri, Daskalakis, Ilyas, and Zampetakis [CDIZ23, STOC’23]. Our main result is a $operatorname{poly}(d,k,1/varepsilon) + {k}^{O(k)}$…

  • Deep spatio-temporal point processes: Advances and new directions

    Deep spatio-temporal point processes: Advances and new directions arXiv:2504.06364v1 Announce Type: new Abstract: Spatio-temporal point processes (STPPs) model discrete events distributed in time and space, with important applications in areas such as criminology, seismology, epidemiology, and social networks. Traditional models often rely on parametric kernels, limiting their ability to capture heterogeneous, nonstationary dynamics. Recent innovations…

  • Sparsified-Learning for Heavy-Tailed Locally Stationary Processes

    Sparsified-Learning for Heavy-Tailed Locally Stationary Processes arXiv:2504.06477v1 Announce Type: new Abstract: Sparsified Learning is ubiquitous in many machine learning tasks. It aims to regularize the objective function by adding a penalization term that considers the constraints made on the learned parameters. This paper considers the problem of learning heavy-tailed LSP. We develop a flexible and…

  • High-dimensional ridge regression with random features for non-identically distributed data with a variance profile

    High-dimensional ridge regression with random features for non-identically distributed data with a variance profile arXiv:2504.03035v1 Announce Type: new Abstract: The behavior of the random feature model in the high-dimensional regression framework has become a popular issue of interest in the machine learning literature}. This model is generally considered for feature vectors $x_i = Sigma^{1/2} x_i’$,…

  • A computational transition for detecting multivariate shuffled linear regression by low-degree polynomials

    A computational transition for detecting multivariate shuffled linear regression by low-degree polynomials arXiv:2504.03097v1 Announce Type: new Abstract: In this paper, we study the problem of multivariate shuffled linear regression, where the correspondence between predictors and responses in a linear model is obfuscated by a latent permutation. Specifically, we investigate the model $Y=tfrac{1}{sqrt{1+sigma^2}}(Pi_* X Q_* +…

  • Rolled Gaussian process models for curves on manifolds

    Rolled Gaussian process models for curves on manifolds arXiv:2503.21980v1 Announce Type: cross Abstract: Given a planar curve, imagine rolling a sphere along that curve without slipping or twisting, and by this means tracing out a curve on the sphere. It is well known that such a rolling operation induces a local isometry between the sphere…

  • Constraint-based causal discovery with tiered background knowledge and latent variables in single or overlapping datasets

    Constraint-based causal discovery with tiered background knowledge and latent variables in single or overlapping datasets arXiv:2503.21526v1 Announce Type: new Abstract: In this paper we consider the use of tiered background knowledge within constraint based causal discovery. Our focus is on settings relaxing causal sufficiency, i.e. allowing for latent variables which may arise because relevant information…

  • A Statistical Theory of Contrastive Learning via Approximate Sufficient Statistics

    A Statistical Theory of Contrastive Learning via Approximate Sufficient Statistics arXiv:2503.17538v1 Announce Type: new Abstract: Contrastive learning — a modern approach to extract useful representations from unlabeled data by training models to distinguish similar samples from dissimilar ones — has driven significant progress in foundation models. In this work, we develop a new theoretical framework…

  • Poisson-Process Topic Model for Integrating Knowledge from Pre-trained Language Models

    Poisson-Process Topic Model for Integrating Knowledge from Pre-trained Language Models arXiv:2503.17809v1 Announce Type: new Abstract: Topic modeling is traditionally applied to word counts without accounting for the context in which words appear. Recent advancements in large language models (LLMs) offer contextualized word embeddings, which capture deeper meaning and relationships between words. We aim to leverage…

  • Optimal Nonlinear Online Learning under Sequential Price Competition via s-Concavity

    Optimal Nonlinear Online Learning under Sequential Price Competition via s-Concavity arXiv:2503.16737v1 Announce Type: new Abstract: We consider price competition among multiple sellers over a selling horizon of $T$ periods. In each period, sellers simultaneously offer their prices and subsequently observe their respective demand that is unobservable to competitors. The demand function for each seller depends…

  • Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling

    Nonlinear Bayesian Update via Ensemble Kernel Regression with Clustering and Subsampling arXiv:2503.15160v1 Announce Type: new Abstract: Nonlinear Bayesian update for a prior ensemble is proposed to extend traditional ensemble Kalman filtering to settings characterized by non-Gaussian priors and nonlinear measurement operators. In this framework, the observed component is first denoised via a standard Kalman update,…

  • Addressing pitfalls in implicit unobserved confounding synthesis using explicit block hierarchical ancestral sampling

    Addressing pitfalls in implicit unobserved confounding synthesis using explicit block hierarchical ancestral sampling arXiv:2503.09194v1 Announce Type: new Abstract: Unbiased data synthesis is crucial for evaluating causal discovery algorithms in the presence of unobserved confounding, given the scarcity of real-world datasets. A common approach, implicit parameterization, encodes unobserved confounding by modifying the off-diagonal entries of the…

  • Personalized Convolutional Dictionary Learning of Physiological Time Series

    Personalized Convolutional Dictionary Learning of Physiological Time Series arXiv:2503.07687v1 Announce Type: new Abstract: Human physiological signals tend to exhibit both global and local structures: the former are shared across a population, while the latter reflect inter-individual variability. For instance, kinetic measurements of the gait cycle during locomotion present common characteristics, although idiosyncrasies may be observed…

  • Learning Causal Response Representations through Direct Effect Analysis

    Learning Causal Response Representations through Direct Effect Analysis arXiv:2503.04358v1 Announce Type: new Abstract: We propose a novel approach for learning causal response representations. Our method aims to extract directions in which a multidimensional outcome is most directly caused by a treatment variable. By bridging conditional independence testing with causal representation learning, we formulate an optimisation…

  • Conformal Prediction Under Generalized Covariate Shift with Posterior Drift

    Conformal Prediction Under Generalized Covariate Shift with Posterior Drift arXiv:2502.17744v1 Announce Type: new Abstract: In many real applications of statistical learning, collecting sufficiently many training data is often expensive, time-consuming, or even unrealistic. In this case, a transfer learning approach, which aims to leverage knowledge from a related source domain to improve the learning performance…

  • Rectifying Conformity Scores for Better Conditional Coverage

    Rectifying Conformity Scores for Better Conditional Coverage arXiv:2502.16336v1 Announce Type: new Abstract: We present a new method for generating confidence sets within the split conformal prediction framework. Our method performs a trainable transformation of any given conformity score to improve conditional coverage while ensuring exact marginal coverage. The transformation is based on an estimate of…

  • Tensor Product Neural Networks for Functional ANOVA Model

    Tensor Product Neural Networks for Functional ANOVA Model arXiv:2502.15215v1 Announce Type: new Abstract: Interpretability for machine learning models is becoming more and more important as machine learning models become more complex. The functional ANOVA model, which decomposes a high-dimensional function into a sum of lower dimensional functions so called components, is one of the most…

  • Conformal Prediction under L’evy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations

    Conformal Prediction under L’evy-Prokhorov Distribution Shifts: Robustness to Local and Global Perturbations arXiv:2502.14105v1 Announce Type: new Abstract: Conformal prediction provides a powerful framework for constructing prediction intervals with finite-sample guarantees, yet its robustness under distribution shifts remains a significant challenge. This paper addresses this limitation by modeling distribution shifts using L’evy-Prokhorov (LP) ambiguity sets, which…

  • An Efficient Permutation-Based Kernel Two-Sample Test

    An Efficient Permutation-Based Kernel Two-Sample Test arXiv:2502.13570v1 Announce Type: new Abstract: Two-sample hypothesis testing-determining whether two sets of data are drawn from the same distribution-is a fundamental problem in statistics and machine learning with broad scientific applications. In the context of nonparametric testing, maximum mean discrepancy (MMD) has gained popularity as a test statistic due…

  • Forecasting time series with constraints

    Forecasting time series with constraints arXiv:2502.10485v1 Announce Type: new Abstract: Time series forecasting presents unique challenges that limit the effectiveness of traditional machine learning algorithms. To address these limitations, various approaches have incorporated linear constraints into learning algorithms, such as generalized additive models and hierarchical forecasting. In this paper, we propose a unified framework for…

  • Algorithmic contiguity from low-degree conjecture and applications in correlated random graphs

    Algorithmic contiguity from low-degree conjecture and applications in correlated random graphs arXiv:2502.09832v1 Announce Type: new Abstract: In this paper, assuming a natural strengthening of the low-degree conjecture, we provide evidence of computational hardness for two problems: (1) the (partial) matching recovery problem in the sparse correlated ErdH{o}s-R’enyi graphs $mathcal G(n,q;rho)$ when the edge-density $q=n^{-1+o(1)}$ and…

  • Riemannian Proximal Sampler for High-accuracy Sampling on Manifolds

    Riemannian Proximal Sampler for High-accuracy Sampling on Manifolds arXiv:2502.07265v1 Announce Type: new Abstract: We introduce the Riemannian Proximal Sampler, a method for sampling from densities defined on Riemannian manifolds. The performance of this sampler critically depends on two key oracles: the Manifold Brownian Increments (MBI) oracle and the Riemannian Heat-kernel (RHK) oracle. We establish high-accuracy…

  • Poisson Hierarchical Indian Buffet Processes for Within and Across Group Sharing of Latent Features-With Indications for Microbiome Species Sampling Models

    Poisson Hierarchical Indian Buffet Processes for Within and Across Group Sharing of Latent Features-With Indications for Microbiome Species Sampling Models arXiv:2502.01919v1 Announce Type: new Abstract: In this work, we present a comprehensive Bayesian posterior analysis of what we term Poisson Hierarchical Indian Buffet Processes, designed for complex random sparse count species sampling models that allow…

  • Local minima of the empirical risk in high dimension: General theorems and convex examples

    Local minima of the empirical risk in high dimension: General theorems and convex examples arXiv:2502.01953v1 Announce Type: new Abstract: We consider a general model for high-dimensional empirical risk minimization whereby the data $mathbf{x}_i$ are $d$-dimensional isotropic Gaussian vectors, the model is parametrized by $mathbf{Theta}inmathbb{R}^{dtimes k}$, and the loss depends on the data via the projection…

  • Supervised Quadratic Feature Analysis: An Information Geometry Approach to Dimensionality Reduction

    Supervised Quadratic Feature Analysis: An Information Geometry Approach to Dimensionality Reduction arXiv:2502.00168v1 Announce Type: new Abstract: Supervised dimensionality reduction aims to map labeled data to a low-dimensional feature space while maximizing class discriminability. Despite the availability of methods for learning complex non-linear features (e.g. Deep Learning), there is an enduring demand for dimensionality reduction methods…

  • Learning to Fuse Temporal Proximity Networks: A Case Study in Chimpanzee Social Interactions

    Learning to Fuse Temporal Proximity Networks: A Case Study in Chimpanzee Social Interactions arXiv:2502.00302v1 Announce Type: new Abstract: How can we identify groups of primate individuals which could be conjectured to drive social structure? To address this question, one of us has collected a time series of data for social interactions between chimpanzees. Here we…

  • Optimal Survey Design for Private Mean Estimation

    Optimal Survey Design for Private Mean Estimation arXiv:2501.18121v1 Announce Type: new Abstract: This work identifies the first privacy-aware stratified sampling scheme that minimizes the variance for general private mean estimation under the Laplace, Discrete Laplace (DLap) and Truncated-Uniform-Laplace (TuLap) mechanisms within the framework of differential privacy (DP). We view stratified sampling as a subsampling operation,…

  • Statistical Verification of Linear Classifiers

    Statistical Verification of Linear Classifiers arXiv:2501.14430v1 Announce Type: new Abstract: We propose a homogeneity test closely related to the concept of linear separability between two samples. Using the test one can answer the question whether a linear classifier is merely “random” or effectively captures differences between two classes. We focus on establishing upper bounds for…

  • Singular leaning coefficients and efficiency in learning theory

    Singular leaning coefficients and efficiency in learning theory arXiv:2501.12747v1 Announce Type: new Abstract: Singular learning models with non-positive Fisher information matrices include neural networks, reduced-rank regression, Boltzmann machines, normal mixture models, and others. These models have been widely used in the development of learning machines. However, theoretical analysis is still in its early stages. In…

  • SBAMDT: Bayesian Additive Decision Trees with Adaptive Soft Semi-multivariate Split Rules

    SBAMDT: Bayesian Additive Decision Trees with Adaptive Soft Semi-multivariate Split Rules arXiv:2501.09900v1 Announce Type: new Abstract: Bayesian Additive Regression Trees [BART, Chipman et al., 2010] have gained significant popularity due to their remarkable predictive performance and ability to quantify uncertainty. However, standard decision tree models rely on recursive data splits at each decision node, using…

  • Generative Models with ELBOs Converging to Entropy Sums

    Generative Models with ELBOs Converging to Entropy Sums arXiv:2501.09022v1 Announce Type: new Abstract: The evidence lower bound (ELBO) is one of the most central objectives for probabilistic unsupervised learning. For the ELBOs of several generative models and model classes, we here prove convergence to entropy sums. As one result, we provide a list of generative…

  • Estimating shared subspace with AJIVE: the power and limitation of multiple data matrices

    Estimating shared subspace with AJIVE: the power and limitation of multiple data matrices arXiv:2501.09336v1 Announce Type: new Abstract: Integrative data analysis often requires disentangling joint and individual variations across multiple datasets, a challenge commonly addressed by the Joint and Individual Variation Explained (JIVE) model. While numerous methods have been developed to estimate the shared subspace…

  • On the Statistical Capacity of Deep Generative Models

    On the Statistical Capacity of Deep Generative Models arXiv:2501.07763v1 Announce Type: new Abstract: Deep generative models are routinely used in generating samples from complex, high-dimensional distributions. Despite their apparent successes, their statistical properties are not well understood. A common assumption is that with enough training data and sufficiently large neural networks, deep generative model samples…

  • Mixing Times and Privacy Analysis for the Projected Langevin Algorithm under a Modulus of Continuity

    Mixing Times and Privacy Analysis for the Projected Langevin Algorithm under a Modulus of Continuity arXiv:2501.04134v1 Announce Type: new Abstract: We study the mixing time of the projected Langevin algorithm (LA) and the privacy curve of noisy Stochastic Gradient Descent (SGD), beyond nonexpansive iterations. Specifically, we derive new mixing time bounds for the projected LA…

  • Robust random graph matching in dense graphs via vector approximate message passing

    Robust random graph matching in dense graphs via vector approximate message passing arXiv:2412.16457v1 Announce Type: new Abstract: In this paper, we focus on the matching recovery problem between a pair of correlated Gaussian Wigner matrices with a latent vertex correspondence. We are particularly interested in a robust version of this problem such that our observation…

  • Learning sparsity-promoting regularizers for linear inverse problems

    Learning sparsity-promoting regularizers for linear inverse problems arXiv:2412.16031v1 Announce Type: new Abstract: This paper introduces a novel approach to learning sparsity-promoting regularizers for solving linear inverse problems. We develop a bilevel optimization framework to select an optimal synthesis operator, denoted as $B$, which regularizes the inverse problem while promoting sparsity in the solution. The method…

  • A Statistical Analysis for Supervised Deep Learning with Exponential Families for Intrinsically Low-dimensional Data

    A Statistical Analysis for Supervised Deep Learning with Exponential Families for Intrinsically Low-dimensional Data arXiv:2412.09779v1 Announce Type: new Abstract: Recent advances have revealed that the rate of convergence of the expected test error in deep supervised learning decays as a function of the intrinsic dimension and not the dimension $d$ of the input space. Existing…

  • On the Precise Asymptotics and Refined Regret of the Variance-Aware UCB Algorithm

    On the Precise Asymptotics and Refined Regret of the Variance-Aware UCB Algorithm arXiv:2412.08843v1 Announce Type: new Abstract: In this paper, we study the behavior of the Upper Confidence Bound-Variance (UCB-V) algorithm for Multi-Armed Bandit (MAB) problems, a variant of the canonical Upper Confidence Bound (UCB) algorithm that incorporates variance estimates into its decision-making process. More…

  • Belted and Ensembled Neural Network for Linear and Nonlinear Sufficient Dimension Reduction

    Belted and Ensembled Neural Network for Linear and Nonlinear Sufficient Dimension Reduction arXiv:2412.08961v1 Announce Type: new Abstract: We introduce a unified, flexible, and easy-to-implement framework of sufficient dimension reduction that can accommodate both linear and nonlinear dimension reduction, and both the conditional distribution and the conditional mean as the targets of estimation. This unified framework…

  • How well behaved is finite dimensional Diffusion Maps?

    How well behaved is finite dimensional Diffusion Maps? arXiv:2412.03992v1 Announce Type: new Abstract: Under a set of assumptions on a family of submanifolds $subset {mathbb R}^D$, we derive a series of geometric properties that remain valid after finite-dimensional and almost isometric Diffusion Maps (DM), including almost uniform density, finite polynomial approximation and local reach. Leveraging…

  • Pathwise optimization for bridge-type estimators and its applications

    Pathwise optimization for bridge-type estimators and its applications arXiv:2412.04047v1 Announce Type: new Abstract: Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any possible value of the penalization parameter $lambda$. In…

  • The Broader Landscape of Robustness in Algorithmic Statistics

    The Broader Landscape of Robustness in Algorithmic Statistics arXiv:2412.02670v1 Announce Type: new Abstract: The last decade has seen a number of advances in computationally efficient algorithms for statistical methods subject to robustness constraints. An estimator may be robust in a number of different ways: to contamination of the dataset, to heavy-tailed data, or in the…

  • A Flexible Defense Against the Winner’s Curse

    A Flexible Defense Against the Winner’s Curse arXiv:2411.18569v1 Announce Type: new Abstract: Across science and policy, decision-makers often need to draw conclusions about the best candidate among competing alternatives. For instance, researchers may seek to infer the effectiveness of the most successful treatment or determine which demographic group benefits most from a specific treatment. Similarly,…